Show all steps in the solutions to the following problems. Insufficient justification will result in a loss of marks. Please indicate all indeterminate forms encountered and any points at which L'Hospital's Rule is applied. 1. [5 marks] There is a class of functions called hyperbolic functions, one of which is coth(x) ex - e-x) known as the hyperbolic cotangent function. (a) Notice that lim coth(x) = lim e tex x -+ 0 x-+0 er - e-x - has an indeterminate form of -. Apply L'Hospital's rule once but do not evaluate the resulting limit. (b) Notice that the result from part (a) has an indeterminate form of -. Apply L'Hospital's rule a second time but do not evaluate the resulting limit. Comparing the result to the limit in (a), what has occurred? (c) Rewrite the lim coth(x) using the substitution t = et (when x - co then et - co and thus t - co) and then evaluate the limit, using L'Hospital's rule if applicable